1. Make a conjecture as to who you think is correct, father or the son.
2. Justify that your conjecture is true for any quadrilateral using theorems of grometry shown below.
3. Which shape is the most efficient?
Why don't you draw it with a pair of compass on a bit of paper and then you will see.
If you do not have compasses you could use a computer program or a lid to draw the cirles.
The diameter of the lid will be the lenth of the side of the square.
Oh, i just realised that it does not have to be a square.
That will make you think harder .....